標題: Titlebook: Classical Potential Theory and Its Probabilistic Counterpart; Joseph L. Doob Book 2001 Springer-Verlag Berlin Heidelberg 2001 31XX.Brownia [打印本頁] 作者: 明顯 時間: 2025-3-21 18:52
書目名稱Classical Potential Theory and Its Probabilistic Counterpart影響因子(影響力)
書目名稱Classical Potential Theory and Its Probabilistic Counterpart影響因子(影響力)學科排名
書目名稱Classical Potential Theory and Its Probabilistic Counterpart網(wǎng)絡(luò)公開度
書目名稱Classical Potential Theory and Its Probabilistic Counterpart網(wǎng)絡(luò)公開度學科排名
書目名稱Classical Potential Theory and Its Probabilistic Counterpart被引頻次
書目名稱Classical Potential Theory and Its Probabilistic Counterpart被引頻次學科排名
書目名稱Classical Potential Theory and Its Probabilistic Counterpart年度引用
書目名稱Classical Potential Theory and Its Probabilistic Counterpart年度引用學科排名
書目名稱Classical Potential Theory and Its Probabilistic Counterpart讀者反饋
書目名稱Classical Potential Theory and Its Probabilistic Counterpart讀者反饋學科排名
作者: 從容 時間: 2025-3-22 00:02
Parabolic Potential Theory: Basic Factss the set of points of . that are endpoints of continuous [strictly] downward-directed arcs from ξ?. That is, η? is [strictly] below ξ? relative to ? if and only if there is a continuous function . from [0, 1] into ? for which .(0)=ξ?, .(1)=η?, and ord . is a [strictly] decreasing function. The . of作者: 清澈 時間: 2025-3-22 03:26
Places/Non-places: Galicia on the ,uclidean topology. Since the fine topology is defined intrinsically in terms of superharmonic functions, it is not surprising that this topology plays a fundamental role in classical potential theory.作者: ANIM 時間: 2025-3-22 07:41 作者: trigger 時間: 2025-3-22 11:10
Classical Potential Theory and Its Probabilistic Counterpart作者: 粘土 時間: 2025-3-22 15:21 作者: 粘土 時間: 2025-3-22 17:47 作者: 可忽略 時間: 2025-3-23 01:07 作者: 一條卷發(fā) 時間: 2025-3-23 01:37 作者: encyclopedia 時間: 2025-3-23 09:14 作者: 獨行者 時間: 2025-3-23 13:28 作者: Heretical 時間: 2025-3-23 14:56
Introduction to the Mathematical Background of Classical Potential TheoryIn this chapter some of the mathematical ideas of classical potential theory are introduced, under simplifying assumptions. The basic space is Euclidean . space ?.. For a ball .(ξ, δ) in ?.作者: 時間等 時間: 2025-3-23 18:49 作者: patella 時間: 2025-3-23 22:32 作者: 名義上 時間: 2025-3-24 02:49
The Fundamental Convergence Theorem and the Reduction Operation.. Let Γ: {u., α ∈ I} be a family of superharmonic functions defined on an open subset of ?., locally uniformly bounded below, and define the lower envelope u by u(ξ) = ..u.(ξ). Then .u ≤ u, ..作者: landmark 時間: 2025-3-24 09:56 作者: corporate 時間: 2025-3-24 14:29
The Martin BoundaryLet . be an open subset of ?.. If . is a ball, its Euclidean boundary is so well adapted to it from a potential theoretic point of view that the following statements are true.作者: 使堅硬 時間: 2025-3-24 15:39 作者: 臭名昭著 時間: 2025-3-24 20:12
978-3-540-41206-9Springer-Verlag Berlin Heidelberg 2001作者: prodrome 時間: 2025-3-25 03:04
Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions = δ.. To simplify the notation take ξ. = .. Then .., as defined by.with the understanding that ..(ξ, ξ)= +∞, satisfies items (ix′)–(ivx′) of Section 1.8, so that harmonic measure for . is given by.where .. here refers to surface area on ?. and作者: Neutropenia 時間: 2025-3-25 03:31
Polar Sets and Their Applicationsch point of the set in the neighborhood. An . set is a set whose compact subsets are polar. It will be shown in Section VI.2 that an analytic inner polar set is polar. If a set is (inner) polar its Kelvin transforms are also.作者: 耐寒 時間: 2025-3-25 08:18 作者: 擴音器 時間: 2025-3-25 15:11
Classical Energy and Capacityductor, if . is a connected conducting body in ?., the charge on . distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in ?. is a constant function.作者: 一瞥 時間: 2025-3-25 15:49 作者: parallelism 時間: 2025-3-25 20:32
Subparabolic, Superparabolic, and Parabolic Functions on a SlabXV. 7 for smooth regions. It is therefore to be expected from XV (7.3) that the upper boundary of ? if δ<+∞ is a parabolic measure null set and that parabolic measure on the lower boundary is given by. so that if u? is parabolic on ? with boundary function . in some suitable sense on the lower boundary and if u? is appropriately restricted, then作者: 雪上輕舟飛過 時間: 2025-3-26 03:06
Parabolic Potential Theory (Continued)if there is one, is denoted by ?M.Γ [?M.Γ]. For example, if Γ is a class of superparabolic functions and if Γ has a subparabolic minorant then ?M.Γ exists and is parabolic. The proof is a translation of that of Theorem III.2. The corresponding notation in the coparabolic context is . and..作者: 發(fā)展 時間: 2025-3-26 05:36
The Parabolic Dirichlet Problem, Sweeping, and Exceptional Sets if v? is parabolic, superparabolic, or subparabolic, respectively. The notation will be parallel to that in the classical context, with ? omitted when ? ≡ 1. Thus.,.,.,. … need no further identification. In the dual context in which ? is coparabolic we write.,.,.,., …作者: Sinus-Node 時間: 2025-3-26 09:42 作者: Deadpan 時間: 2025-3-26 14:35 作者: ellagic-acid 時間: 2025-3-26 20:10 作者: ANTI 時間: 2025-3-26 21:43
Heidi Kelley,Kenneth A. Betsalelnt ξ of . is assigned some set (perhaps empty) {μ. (ξ, ·), α ∈ ..} of probability measures on .. Call a function . if it satisfies specified smoothness conditions and if.for ξ in . and α in ... For example, if . is an open subset of ?., if for each ξ the index α represents a ball . of center ξ with 作者: Inscrutable 時間: 2025-3-27 03:03
https://doi.org/10.1007/978-3-319-65729-5d the boundary of a subset of . ∪ ?. is that relative to the compactification. In most of the discussion the nature of the boundary is irrelevant, and ?. can be taken, for example, as the Euclidean boundary or one-point boundary of ..作者: Hyperalgesia 時間: 2025-3-27 08:23
Places/Non-places: Galicia on the , then .. is said to be . than ..) if .. ? ... For any family of extended real-valued functions on a space there is a coarsest topology making every member of the family continuous, namely, the intersection of all the topologies doing this. The . topology of classical potential theory is defined as t作者: braggadocio 時間: 2025-3-27 09:35
Festschriftoffener Brief an den Herausgeberductor, if . is a connected conducting body in ?., the charge on . distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in作者: 遠地點 時間: 2025-3-27 17:00 作者: Confirm 時間: 2025-3-27 20:33 作者: 旁觀者 時間: 2025-3-28 00:47
Festschriftoffener Brief an den HerausgeberXV. 7 for smooth regions. It is therefore to be expected from XV (7.3) that the upper boundary of ? if δ<+∞ is a parabolic measure null set and that parabolic measure on the lower boundary is given by. so that if u? is parabolic on ? with boundary function . in some suitable sense on the lower bound作者: seroma 時間: 2025-3-28 02:10 作者: 小鹿 時間: 2025-3-28 08:22
Estimating Population Parameters, if v? is parabolic, superparabolic, or subparabolic, respectively. The notation will be parallel to that in the classical context, with ? omitted when ? ≡ 1. Thus.,.,.,. … need no further identification. In the dual context in which ? is coparabolic we write.,.,.,., …作者: pacifist 時間: 2025-3-28 11:25 作者: 可轉(zhuǎn)變 時間: 2025-3-28 14:52
Classics in Mathematicshttp://image.papertrans.cn/c/image/227122.jpg作者: 夸張 時間: 2025-3-28 19:05
Classical Potential Theory and Its Probabilistic Counterpart978-3-642-56573-1Series ISSN 1431-0821 Series E-ISSN 2512-5257 作者: CESS 時間: 2025-3-29 02:03
https://doi.org/10.1057/9780230106116 = δ.. To simplify the notation take ξ. = .. Then .., as defined by.with the understanding that ..(ξ, ξ)= +∞, satisfies items (ix′)–(ivx′) of Section 1.8, so that harmonic measure for . is given by.where .. here refers to surface area on ?. and作者: Fillet,Filet 時間: 2025-3-29 05:30 作者: MINT 時間: 2025-3-29 09:01 作者: neutrophils 時間: 2025-3-29 12:32
Festschriftoffener Brief an den Herausgeberductor, if . is a connected conducting body in ?., the charge on . distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in ?. is a constant function.作者: 非實體 時間: 2025-3-29 17:21
Festschriftoffener Brief an den Herausgeber is so elementary that it will be left to the reader to formulate and justify. A ball in ? with center ξ is an open interval with midpoint ξ, and the averages .(., ξ, δ), and ... can play the same role when .=1 as when .>1, but more direct methods are sometimes clearer.作者: Minatory 時間: 2025-3-29 20:47 作者: 招待 時間: 2025-3-30 03:57
Multiple Variables and Multiple Hypotheses,if there is one, is denoted by ?M.Γ [?M.Γ]. For example, if Γ is a class of superparabolic functions and if Γ has a subparabolic minorant then ?M.Γ exists and is parabolic. The proof is a translation of that of Theorem III.2. The corresponding notation in the coparabolic context is . and..作者: 深淵 時間: 2025-3-30 07:03
Estimating Population Parameters, if v? is parabolic, superparabolic, or subparabolic, respectively. The notation will be parallel to that in the classical context, with ? omitted when ? ≡ 1. Thus.,.,.,. … need no further identification. In the dual context in which ? is coparabolic we write.,.,.,., …作者: employor 時間: 2025-3-30 11:00
The Dirichlet Problem for Relative Harmonic Functionsclosure in ., if .. is the class of all such balls, and if μ.(ξ, .) is the unweighted average of . on ?., then the class of continuous functions on . satisfying (1.1) is the class of harmonic functions on .. Going back to the general case, suppose that . is a strictly positive generalized harmonic function and define μ..(ξ, ·) by作者: condone 時間: 2025-3-30 13:36
Book 2001liminary knowledge. ...The purpose which the author explains in his introduction, i.e. a deep probabilistic interpretation of potential theory and a link between two great theories, appears fulfilled in a masterly manner"..M. Brelot in Metrika (1986)作者: 多余 時間: 2025-3-30 16:48
Book 2001not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with original complements. This requires no pre作者: Locale 時間: 2025-3-30 22:13 作者: 砍伐 時間: 2025-3-31 00:55
Heidi Kelley,Kenneth A. Betsalelclosure in ., if .. is the class of all such balls, and if μ.(ξ, .) is the unweighted average of . on ?., then the class of continuous functions on . satisfying (1.1) is the class of harmonic functions on .. Going back to the general case, suppose that . is a strictly positive generalized harmonic function and define μ..(ξ, ·) by作者: flamboyant 時間: 2025-3-31 07:13
1431-0821 appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with作者: 作繭自縛 時間: 2025-3-31 11:51 作者: acrophobia 時間: 2025-3-31 15:29
Green Functionsists for every ξ in .. In fact .(ξ , ·)–.(ξ, ·) is bounded below outside each neighborhood of ξ, and .(ξ, ·) is bounded below on each compact neighborhood of ξ so that if GM..(ξ, ·) exists, .(ξ , ·) ≥ . + GM..(ξ, ·) GM..(ξ , ·) ≥ . + GM..(ξ, ·) for some constant . depending on ξand ξ.作者: Magisterial 時間: 2025-3-31 20:09
Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions = δ.. To simplify the notation take ξ. = .. Then .., as defined by.with the understanding that ..(ξ, ξ)= +∞, satisfies items (ix′)–(ivx′) of Section 1.8, so that harmonic measure for . is given by.where .. here refers to surface area on ?. and作者: 愛好 時間: 2025-4-1 01:03
